• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1994년도 Proceedings of the Korea Automatic Control Conference, 9th (KACC) ; Taejeon, Korea; 17-20 Oct. 1994
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• pp.156-161
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• 1994

In this paper, we consider an optimal control problem of a nonlinear stochastic system. Dynamic programming approach is employed for the formulation of a stochastic optimal control problem. As an optimality condition, dynamic programming equation so called the Bellman equation is obtained, which seldom yields an analytical solution, even very difficult to solve numerically. We obtain the numerical solution of the Bellman equation using an algorithm based on the finite difference approximation and the contraction mapping method. Optimal controls are constructed through the solution process of the Bellman equation. We also construct a test case in order to investigate the actual performance of the algorithm.

• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.215-222
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• 2021

We explore an optimal consumption/portfolio and retirement problem with a CARA utility function of consumption. The relevant Bellman equation for the value function is transformed into a linear equation and the optimal strategies are obtained explicitly.

• 제어로봇시스템학회논문지
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• 제4권6호
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• pp.703-706
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• 1998

본 논문에서는 확률 최적 제어문제에서 발생되는 Elliptic type H-J-B(Hamilton-Jacobi-Bellman) 방정식에 대한 수치해를 구하였다. 수치해를 구하기 위하여 Contraction 사상 및 유한차분법을 이용하였으며, 시스템은 It/sub ∧/ 형태의 Stochastic 방정식으로 취하였다. 수치해는 수학적인 테스트 케이스를 설정하여 검증하였으며, 최적제어 Map을 방정식의 해를 구하면서 동시에 구하였다.

• 호남수학학술지
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• 제45권1호
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• pp.54-70
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• 2023

In this article, we state and prove several new retarded nonlinear integral and integro-differential inequalities of Gronwall-Bellman-Pachpatte type. These inequalities generalize some former famous inequalities and can be used in examining the existence, uniqueness, boundedness, stability, asymptotic behaviour, quantitative and qualitative properties of solutions of nonlinear differential and integral equations. Applications are provided to demonstrate the strength of our inequalities in estimating the boundedness and global existence of the solution to initial value problem for nonlinear integro-differential equation and Volterra type retarded nonlinear equation. This research work will ensure to open the new opportunities for studying of nonlinear dynamic inequalities on time scale structure of varying nature.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
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• pp.440-444
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• 1998

In this paper, we consider numerical solution of a H-J-B (Hamilton-Jacobi-Bellman) equation of elliptic type arising from the stochastic control problem. For the numerical solution of the equation, we take an approach involving contraction mapping and finite difference approximation. We choose the It(equation omitted) type stochastic differential equation as the dynamic system concerned. The numerical method of solution is validated computationally by using the constructed test case. Map of optimal controls is obtained through the numerical solution process of the equation. We also show how the method applies by taking a simple example of nonlinear spacecraft control.

• East Asian mathematical journal
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• 제36권1호
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• pp.91-99
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• 2020

This paper obtains an explicit expression for a debtor's consumption, porfolio and time for filing for bankruptcy when the debtor is subject to upper bound on consumption rate. The utility of consumption is CRRA type and the dynamic programming principle is applied.

• 충청수학회지
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• 제26권3호
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• pp.571-576
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• 2013

In this paper, we solve the optimal investment problem when the investor gets labor income and may have a wage increase. We assume the investor has constant absolute risk aversion(CARA) utility and obtain closed form solutions.

• Korean Journal of Mathematics
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• 제16권2호
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• pp.145-156
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• 2008

When we consider a life insurance company that sells a large number of continuous T-year term life insurance policies, it is important to find an optimal strategy which maximizes the surplus of the insurance company at time T. The purpose of this paper is to give an explicit expression for the optimal reinsurance and investment strategy which maximizes the expected exponential utility of the final value of the surplus at the end of T-th year. To do this we solve the corresponding Hamilton-Jacobi-Bellman equation.

• 대한수학회지
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• 제43권1호
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• pp.11-28
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• 2006

The existence, uniqueness and iterative approximation of solutions for a few classes of functional equations arising in dynamic programming of multistage decision processes are discussed. The results presented in this paper extend, improve and unify the results due to Bellman [2, 3], Bhakta-Choudhury [6], Bhakta-Mitra [7], and Liu [12].

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권1호
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• pp.63-78
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• 2011

In the present paper, we obtain integral inequalities involving the Kurzweil-Stieltjes integrals which generalize Gronwall-Bellman inequality and we use the inequalities to verify existence of solutions of a certain integral equation. Such inequalities will play an important role in the study of impulsively perturbed systems [9].